One known method, for example, from DE 10 36 942 B4 and is based on the fact that the average temperature, determined by means of the through-flow length of an exhaust gas post-treatment unit, for example a catalytic converter, does not give a sufficient basis, at any rate in the dynamic operating mode and with the associated non-homogeneous temperature distribution, for the adjustment of a system comprising an engine and the exhaust gas post-treatment unit in such a way that strict requirements made of the exhaust gas quality are satisfied with the necessary accuracy. Said requirements are to be met in that the exhaust gas post-treatment unit is divided in a model-based fashion in the axial direction into a number of disks, and in that the temperature of each disk is determined as a function of the temperature of the gas which flows against the disk. This is done under the assumption that the radial temperature distribution is constant and an adiabatic transfer of heat occurs between the exhaust gas and the disks of the exhaust gas post-treatment unit.
These assumptions lead, in turn, to certain inaccuracies, in particular as a result of the radial temperature gradient which forms contrary to the assumption, for which reason there is a need for these heat losses to be sensed and also taken into account on an approximate basis.
In a further method for the model-based determination of the temperature distribution of exhaust gas post-treatment units, which is known from DE 10 2009 046 771 A1, the axial temperature profile is initially determined at least in certain areas, and on the basis thereof a multi-dimensional temperature characteristic diagram is in turn calculated, at least in certain areas, on the basis of an analytical relationship. Said relationship can be based on various peripheral conditions such as, for example, an already known temperature and/or properties of the exhaust gas post-treatment unit which are significant for the transfer of heat. The position-dependent temperature can be obtained from the calculated temperature characteristic diagram as a result of which, by virtue of the axial temperature profile and the temperature characteristic diagram, in each case at least one temperature which occurs at any position within the exhaust gas post-treatment unit is obtained.
In DE 10 2006 021 303 B4, it is known, with respect to the acquisition of the temperature distribution in an exhaust gas post-treatment unit, to determine the axial temperature distribution by means of a dynamic heat model and to determine, by means of a kinematic model, the reaction heat which is generated during the exhaust gas post-treatment and results from the conversion of exhaust gas components. This is done in order to improve the quality of the determined temperature distribution with as little computational expenditure as possible. By determining the radial temperature distribution, which occurs perpendicular to the main flow, it is possible here to achieve a further improvement in quality on a case-by-case basis, but this in turn requires a relatively high level of computational expenditure.
DE 103 47 132 A1 discloses a method for estimating the quantity of ammonia stored in a urea-based SCR catalytic converter, on the basis of a dynamic catalytic converter model, and generates the estimate on the basis of measured and estimated values, wherein measured values are made available for this by NOx sensors and temperature sensors arranged upstream and downstream of the catalytic converter, said measured values also permitting information to be obtained about the proportion of ammonia in the exhaust gas downstream of the catalytic converter with respect to the NOx sensor located downstream of the catalytic converter on the basis of the cross-sensitivity to ammonia.
In a corresponding way, in EP 2 025 388 A1 sensors are used for determining measured values at an exhaust gas purification unit which operates with an SCR catalytic converter which is regulated in a model-based fashion with respect to the metering and storage of ammonia while taking into account the measured values.
DE 10 2007 045 263 A1 discloses a method for controlling the reducing agent supply into an exhaust gas post-treatment system of an internal combustion engine having an SCR catalytic converter, an SCR storage model, a control unit and a metering device, which method is intended to permit the quantity of reducing agent fed to the catalytic converter to be optimized independently of measurement variables which can be determined exclusively after the reduction reaction, and by which, with respect to the SCR catalytic converter, a breakthrough of reducing agent is to be avoided at all times. For the control unit, the nitrogen oxide crude emissions, storage temperature and storage filling level are determined as input variables. On the basis thereof, the maximum possible conversion rate is calculated and the ammonia consumed as reducing agent is calculated. Taking this as a basis, the quantity of nitrogen oxides and ammonia which escape via the catalytic converter and a regulating signal, which, when fed back to the SCR storage model, influences, via the storage model, the magnitude of the quantity of reducing agent which is to be sprayed in via the metering device, and which is taken into account together with the spraying quantity which is taken into account in the storage model, by means of the storage model for the storage filling level which forms an input variable for the control unit, are produced.
DE 10 2010 025 382 A1 presents an SCR catalytic converter onto which the reducing agent is sprayed upstream, and whose catalytic converter body is divided into disks transversely with respect to the direction of through-flow in a way analogous to DE 10 36 942 B4. This is done in order to be able to determine essential parameters for the function of the catalytic converter by means of disks as well as to be able to use changes which are significant for the overall result in the following disks, in particular with respect to their capability to store reducing agent, for the overall result.